Statistically Equivalent Level of Safety Modeling

ABSTRACT

Systems and methods are provided for statistically equivalent level of safety modeling. One method includes identifying sub-fleets within a fleet based upon usage profiles, determining a sub-fleet reliability value for each sub-fleet, determining a baseline fleet reliability for the fleet by combining the sub-fleet reliability values on a weighted basis, applying at least one credit to at least one sub-fleet, determining a post-credit sub-fleet reliability value for each sub-fleet based upon the at least one credit, determining a post-credit fleet reliability for the fleet by combining the post-credit sub-fleet reliability values on a weighted basis, comparing the baseline fleet reliability with the post-credit fleet reliability to identify a change in fleet reliability and determining whether the change in fleet reliability is within a predetermined threshold to validate the at least one credit.

TECHNICAL FIELD OF THE DISCLOSURE

The present disclosure relates, in general, to time dependent aircraftreliability and, in particular, to a safety methodology for aircraftfleets utilizing statistically equivalent level of safety modeling toextend scheduled maintenance intervals for structural components basedupon measured usage data of aircraft within the aircraft fleet.

BACKGROUND

Aircraft fleet operators are typically under tremendous pressure tooperate their aircraft fleets as efficiently as possible. To achievedesired safety and reliability requirements, however, conservative usageassumptions are generally used to determine the life limits of variousaircraft components. Usage credit has long been proposed as a means toextend scheduled maintenance intervals in an effort to reducemaintenance cost. These usage credits are typically determined throughevaluation of actual aircraft usage of individual aircraft, which mayhave wide variation from the “usage as severe as expected” model. Whilesuch reliability methods have been used as a means to quantify thesafety of individual aircraft, it has been acknowledged that much of theoverall fleet safety achieved using current fatigue tolerance methods isdue to the conservative nature of usage assumptions.

In one model, proposed usage credit is determined based upon detailedcomponent reliability assessments that produce an absolutecharacterization of reliability or its complement, unreliability, as afunction of service life to determine a life limit that providesacceptable safety. Such absolute assessment models, however, are only asgood as the assumptions on the distributions of strength, loads andusage. In addition, variability in these factors, especially loads, isdifficult to quantify such that absolute reliability methods, no matterhow sophisticated, are difficult to validate. Accordingly, a need hasarisen for an improved safety methodology for extending scheduledmaintenance intervals of aircraft. A need has also arisen for such animproved safety methodology that allows for its level of impact on fleetreliability to be determined.

SUMMARY

One of the goals of a safety methodology that includes usage creditshould be to ensure that a proposed change in component or aircraftairworthiness limitations preserves fleet reliability. Past experiencehas shown that current safe-life fatigue methodology has providedacceptable levels of fleet reliability for over 70 years in commercialrotorcraft operation, so this experience provides a standard by whichother methods can be judged, regardless of the nature of assumptionsmade in the current safe-life fatigue methodology. In the presentdisclosure, an improved safety methodology for extending scheduledmaintenance intervals of aircraft is provided that allows for its levelof impact on fleet reliability to be determined.

In a first aspect, the present disclosure is directed to a statisticallyequivalent level of safety modeling method for structural components ofaircraft within an aircraft fleet having (n) aircraft. The methodincludes (A) identifying a first aircraft sub-fleet based upon a firstusage profile and a second aircraft sub-fleet based upon a second usageprofile, the first aircraft sub-fleet having (m) aircraft and the secondaircraft sub-fleet having (n-m) aircraft; (B) determining a firstreliability value (p₁) for the first aircraft sub-fleet and a secondreliability value (p₂) for the second aircraft sub-fleet; (C)determining a baseline fleet reliability (p_(f1)) for the aircraft fleetaccording to the formula: (p_(F1))=(p₁)^(m)×(p₂)^(n-m); (D) applying acredit to the second aircraft sub-fleet; (E) determining a post-creditreliability value (p_(2C)) for the second aircraft sub-fleet based uponthe credit; (F) determining a post-credit fleet reliability (p_(F2)) forthe aircraft fleet according to the formula:(p_(F2))=(p₁)^(m)×(p_(2C))^(n-m); (G) comparing the baseline fleetreliability (p_(F1)) with the post-credit fleet reliability (p_(F2)) toidentify a change in fleet reliability; and (H) determining whether thechange in fleet reliability is within a predetermined threshold tovalidate the credit applied to the second aircraft sub-fleet.

The method may also include basing usage profiles upon measured usagelevels; using a less extreme usage profile for the second usage profilethan the first usage profile; using time dependent probabilitydistribution functions, time to failure probability distributionfunctions and/or any probability distribution function of discreteand/or continuous random variables including, but not limited to, normaldistribution functions, lognormal distribution functions and Poissondistribution functions; relating the reliability values to one or morestructural components of the aircraft of the first and second aircraftsub-fleets; relating the reliability values to probability distributionfunctions based upon strength, loads and usage of the aircraft of thefirst and second aircraft sub-fleets; selecting the credit from thegroup consisting of life limit shifts, life factors and combinationthereof and/or applying a revised credit if the change in fleetreliability is not within the predetermined threshold then repeatingsteps (E)-(H).

In a second aspect, the present disclosure is directed to astatistically equivalent level of safety modeling method for structuralcomponents of aircraft within an aircraft fleet. The method includesidentifying aircraft sub-fleets within the aircraft fleet based uponaircraft usage profiles, each aircraft sub-fleet having a sub-fleetpopulation; determining a sub-fleet reliability value for each aircraftsub-fleet; determining a baseline fleet reliability for the aircraftfleet by multiplying together the sub-fleet reliability values raised tothe sub-fleet population for each aircraft sub-fleet; applying at leastone credit to at least one aircraft sub-fleet; determining a post-creditsub-fleet reliability value for each aircraft sub-fleet based upon theat least one credit; determining a post-credit fleet reliability for theaircraft fleet by multiplying together the post-credit sub-fleetreliability values raised to the sub-fleet population for each aircraftsub-fleet; comparing the baseline fleet reliability with the post-creditfleet reliability to identify a change in fleet reliability; anddetermining whether the change in fleet reliability is within apredetermined threshold to validate the at least one credit.

In a third aspect, the present disclosure is directed to a statisticallyequivalent level of safety modeling method for structural components ofa system within a system fleet. The method includes identifyingsub-fleets within the fleet based upon usage profiles; determining asub-fleet reliability value for each sub-fleet; determining a baselinefleet reliability for the fleet by combining the sub-fleet reliabilityvalues on a weighted basis; applying at least one credit to at least onesub-fleet; determining a post-credit sub-fleet reliability value foreach sub-fleet based upon the at least one credit; determining apost-credit fleet reliability for the fleet by combining the post-creditsub-fleet reliability values on a weighted basis; comparing the baselinefleet reliability with the post-credit fleet reliability to identify achange in fleet reliability; and determining whether the change in fleetreliability is within a predetermined threshold to validate the at leastone credit. The method may also include establishing the weighted basisbased upon the number of systems in each sub-fleet.

In a fourth aspect, the present disclosure is directed to astatistically equivalent level of safety modeling system for structuralcomponents of aircraft within an aircraft fleet. The system includes astatistically equivalent level of safety modeling computing systemhaving logic stored within a non-transitory computer readable medium,the logic executable by a processor, wherein the statisticallyequivalent level of safety modeling computing system is configured toidentify a first aircraft sub-fleet based upon a first usage profile anda second aircraft sub-fleet based upon a second usage profile, the firstaircraft sub-fleet having (m) aircraft and the second aircraft sub-fleethaving (n-m) aircraft; determine a first reliability value (p₁) for thefirst aircraft sub-fleet and a second reliability value (p₂) for thesecond aircraft sub-fleet; determine a baseline fleet reliability(p_(f1)) for the aircraft fleet according to the formula:(p_(F1))=(p₁)^(m)×(p₂)^(n-m), apply a credit to the second aircraftsub-fleet; determine a post-credit reliability value (p_(2C)) for thesecond aircraft sub-fleet based upon the credit; determine a post-creditfleet reliability (p_(F2)) for the aircraft fleet according to theformula: (p_(F2))=(p₁)^(m)×(p_(2C))^(n-m); compare the baseline fleetreliability (p_(F1)) with the post-credit fleet reliability (p_(F2)) toidentify a change in fleet reliability; and determine whether the changein fleet reliability is within a predetermined threshold to validate thecredit applied to the second aircraft sub-fleet.

In a fifth aspect, the present disclosure is directed to a statisticallyequivalent level of safety modeling system for structural components ofaircraft within an aircraft fleet. The system includes a statisticallyequivalent level of safety modeling computing system having logic storedwithin a non-transitory computer readable medium, the logic executableby a processor, wherein the statistically equivalent level of safetymodeling computing system is configured to identify aircraft sub-fleetswithin the aircraft fleet based upon aircraft usage profiles, eachaircraft sub-fleet having a sub-fleet population; determine a sub-fleetreliability value for each aircraft sub-fleet; determine a baselinefleet reliability for the aircraft fleet by multiplying together thesub-fleet reliability values raised to the sub-fleet population for eachaircraft sub-fleet; apply at least one credit to at least one aircraftsub-fleet; determine a post-credit sub-fleet reliability value for eachaircraft sub-fleet based upon the at least one credit; determine apost-credit fleet reliability for the aircraft fleet by multiplyingtogether the post-credit sub-fleet reliability values raised to thesub-fleet population for each aircraft sub-fleet; compare the baselinefleet reliability with the post-credit fleet reliability to identify achange in fleet reliability; and determine whether the change in fleetreliability is within a predetermined threshold to validate the at leastone credit.

In a sixth aspect, the present disclosure is directed to a statisticallyequivalent level of safety modeling system for structural components ofaircraft within an aircraft fleet. The system includes a statisticallyequivalent level of safety modeling computing system having logic storedwithin a non-transitory computer readable medium, the logic executableby a processor, wherein the statistically equivalent level of safetymodeling computing system is configured to identify sub-fleets withinthe fleet based upon usage profiles; determine a sub-fleet reliabilityvalue for each sub-fleet; determine a baseline fleet reliability for thefleet by combining the sub-fleet reliability values on a weighted basis;apply at least one credit to at least one sub-fleet; determine apost-credit sub-fleet reliability value for each sub-fleet based uponthe at least one credit; determine a post-credit fleet reliability forthe fleet by combining the post-credit sub-fleet reliability values on aweighted basis; compare the baseline fleet reliability with thepost-credit fleet reliability to identify a change in fleet reliability;and determine whether the change in fleet reliability is within apredetermined threshold to validate the at least one credit.

In a seventh aspect, the present disclosure is directed to anon-transitory computer readable storage medium comprising a set ofcomputer instructions executable by a processor for operating astatistically equivalent level of safety modeling system. The computerinstructions are configured to identify a first aircraft sub-fleet basedupon a first usage profile and a second aircraft sub-fleet based upon asecond usage profile, the first aircraft sub-fleet having (m) aircraftand the second aircraft sub-fleet having (n-m) aircraft; determine afirst reliability value (p₁) for the first aircraft sub-fleet and asecond reliability value (p₂) for the second aircraft sub-fleet;determine a baseline fleet reliability (p_(f1)) for the aircraft fleetaccording to the formula: (p_(F1))=(p₁)^(m)×(p₂)^(n-m); apply a creditto the second aircraft sub-fleet; determine a post-credit reliabilityvalue (p_(2C)) for the second aircraft sub-fleet based upon the credit;determine a post-credit fleet reliability (p_(F2)) for the aircraftfleet according to the formula: (p_(F2))=(p₁)^(m)×(p_(2C))^(n-m);compare the baseline fleet reliability (p_(F1)) with the post-creditfleet reliability (p_(F2)) to identify a change in fleet reliability;and determine whether the change in fleet reliability is within apredetermined threshold to validate the credit applied to the secondaircraft sub-fleet.

In an eighth aspect, the present disclosure is directed to anon-transitory computer readable storage medium comprising a set ofcomputer instructions executable by a processor for operating astatistically equivalent level of safety modeling system. The computerinstructions are configured to identify aircraft sub-fleets within theaircraft fleet based upon aircraft usage profiles, each aircraftsub-fleet having a sub-fleet population; determine a sub-fleetreliability value for each aircraft sub-fleet; determine a baselinefleet reliability for the aircraft fleet by multiplying together thesub-fleet reliability values raised to the sub-fleet population for eachaircraft sub-fleet; apply at least one credit to at least one aircraftsub-fleet; determine a post-credit sub-fleet reliability value for eachaircraft sub-fleet based upon the at least one credit; determine apost-credit fleet reliability for the aircraft fleet by multiplyingtogether the post-credit sub-fleet reliability values raised to thesub-fleet population for each aircraft sub-fleet; compare the baselinefleet reliability with the post-credit fleet reliability to identify achange in fleet reliability; and determine whether the change in fleetreliability is within a predetermined threshold to validate the at leastone credit.

In a ninth aspect, the present disclosure is directed to anon-transitory computer readable storage medium comprising a set ofcomputer instructions executable by a processor for operating astatistically equivalent level of safety modeling system. The computerinstructions are configured to identify sub-fleets within the fleetbased upon usage profiles; determine a sub-fleet reliability value foreach sub-fleet; determine a baseline fleet reliability for the fleet bycombining the sub-fleet reliability values on a weighted basis; apply atleast one credit to at least one sub-fleet; determine a post-creditsub-fleet reliability value for each sub-fleet based upon the at leastone credit; determine a post-credit fleet reliability for the fleet bycombining the post-credit sub-fleet reliability values on a weightedbasis; compare the baseline fleet reliability with the post-credit fleetreliability to identify a change in fleet reliability; and determinewhether the change in fleet reliability is within a predeterminedthreshold to validate the at least one credit.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the features and advantages of thepresent disclosure, reference is now made to the detailed descriptionalong with the accompanying figures in which corresponding numerals inthe different figures refer to corresponding parts and in which:

FIG. 1 is a flow diagram of a statistically equivalent level of safetymodeling system for components or aircraft within an aircraft fleet inaccordance with embodiments of the present disclosure;

FIG. 2 is a time to failure probability distribution for components oraircraft within an aircraft fleet in accordance with embodiments of thepresent disclosure;

FIG. 3 is a schematic illustration of an aircraft fleet split into twoaircraft sub-fleets in accordance with embodiments of the presentdisclosure;

FIGS. 4A-4B show time to failure probability distributions relating tocomponents or aircraft in two aircraft sub-fleets within an aircraftfleet in accordance with embodiments of the present disclosure;

FIGS. 5-6 are Credit Hours versus Fleet Unreliability plots relating tocomponents or aircraft within an aircraft fleet in accordance withembodiments of the present disclosure;

FIG. 7 is a flow diagram of a process of statistically equivalent levelof safety modeling relating to components or aircraft within an aircraftfleet in accordance with embodiments of the present disclosure;

FIG. 8 is a Total Flight Hours versus High Altitude Flight Hours plotsrelating to components or aircraft within an aircraft fleet inaccordance with embodiments of the present disclosure;

FIG. 9 is a flow diagram of a process of determining componentreliability for aircraft sub-fleets within an aircraft fleet inaccordance with embodiments of the present disclosure;

FIG. 10 is a flow diagram of a process of determining baseline fleetreliability for an aircraft fleet in accordance with embodiments of thepresent disclosure; and

FIG. 11 is a flow diagram of a process of determining post-credit fleetreliability for an aircraft fleet in accordance with embodiments of thepresent disclosure.

DETAILED DESCRIPTION

While the making and using of various embodiments of the presentdisclosure are discussed in detail below, it should be appreciated thatthe present disclosure provides many applicable inventive concepts,which can be embodied in a wide variety of specific contexts. Thespecific embodiments discussed herein are merely illustrative and do notdelimit the scope of the present disclosure. In the interest of clarity,not all features of an actual implementation may be described in thepresent disclosure. It will of course be appreciated that in thedevelopment of any such actual embodiment, numerousimplementation-specific decisions must be made to achieve thedeveloper's specific goals, such as compliance with system-related andbusiness-related constraints, which will vary from one implementation toanother. Moreover, it will be appreciated that such a development effortmight be complex and time-consuming but would be a routine undertakingfor those of ordinary skill in the art having the benefit of thisdisclosure.

Referring to FIG. 1 in the drawings, a flow diagram representing systemsand methods for statistically equivalent level of safety modeling forstructural components of aircraft within an aircraft fleet is generallydesignated 10. The systems and methods described herein provide amechanism for extending scheduled maintenance intervals of aircraft anddetermining the level of impact on fleet reliability of such extensions.This is achieved, in part, by using current safe-life fatiguemethodology 12, which has provided an acceptable level of fleetreliability for over 70 years in commercial rotorcraft operation (see 14C.F.R. 29.571; which is hereby incorporated by reference). The presentsystems and methods utilize current safe-life fatigue methodology 12 asthe standard or baseline against which the disclosed systems and methodsare judged such that adjustments in maintenance intervals or credits canbe validated. In addition, the present systems and methods leveragecurrent safe-life fatigue methodology 12 using many of the sameassumptions, which have been proven to yield overall fleet safety.

Safe-life fatigue methodology 12 utilize a fatigue tolerance evaluation14 to analyze fatigue factors 16 including component strength 18, loads20 and usage 22 relating to each principal structural element of anaircraft. The fatigue tolerance evaluation 14 establishes appropriateinspection intervals and/or retirement time 24 to avoid catastrophicfailure during the operational life of an aircraft. For example, thefatigue tolerance evaluation 14 of principal structural elements mayinclude in-flight measurements to determine the fatigue loads orstresses during all critical conditions throughout the range of designlimitations using a loading spectra as severe as those expected inoperations; a threat assessment which includes a determination of theprobable locations, types and sizes of damage, taking into accountfatigue, environmental effects, intrinsic and discrete flaws, oraccidental damage that may occur during manufacture or operation; and adetermination of the fatigue tolerance characteristics for the principalstructural elements that supports the inspection and retirement times.

In the illustrated embodiment, a statistically equivalent level ofsafety modeling computing system 26 is used to identify sub-fleetswithin an aircraft fleet that may be candidates for a credit to extendinspection intervals and/or retirement time of components or aircraftbased upon usage profiles and to validate the credit based upon thelevel of change in the overall fleet reliability resulting from thecredit. Computing system 26 may be implemented on a general-purposecomputer, a special purpose computer or other machine with memory andprocessing capability. For example, computing system 26 may include oneor more memory storage modules including, but is not limited to,internal storage memory such as random access memory (RAM), non-volatilememory such as read only memory (ROM), removable memory such as magneticstorage memory, optical storage memory including CD and DVD media,solid-state storage memory including CompactFlash cards, Memory Sticks,SmartMedia cards, MultiMediaCards (MMC), Secure Digital (SD) memory orother suitable memory storage entity. Computing system 26 may be amicroprocessor-based system operable to execute program code in the formof machine-executable instructions. In addition, computing system 26 maybe connected to other computer systems via a proprietary encryptednetwork, a public encrypted network, the Internet or other suitablecommunication network that may include both wired and wirelessconnections. The communication network may be a local area network(LAN), wide area network (WAN), the Internet, or any other type ofnetwork that couples a plurality of computers to enable various modes ofcommunication via network messages using as suitable communicationtechnique, such as Transmission Control Protocol/Internet Protocol(TCP/IP), File Transfer Protocol (FTP), Hypertext Transfer Protocol(HTTP), Internet Protocol Security Protocol (IPSec), Point-to-PointTunneling Protocol (PPTP), Secure Sockets Layer (SSL) Protocol or othersuitable protocol.

Computing system 26 preferably includes a display device configured todisplay information including graphical user interfaces. The displaydevice may be configured in any suitable form, including, for example,Liquid Crystal Displays (LCD), Light emitting diode displays (LED),Cathode Ray Tube Displays (CRT) or any suitable type of display.Computing system 26 and/or the display device may also include an audiooutput device such as speakers or an audio port allowing the user tohear audio output. The display device may also serve as a user interfacedevice if a touch screen display implementation is used. Other userinterface devices associated with computing system 26 may include akeyboard and mouse, a keypad, a touch pad, a video camera, a microphoneand the like to allow a user to interact with computing system 26,programs operating on computing system 26 and other computing systems incommunication with computing system 26.

Computing system 26 preferably includes a non-transitory computerreadable storage medium including a set of computer instructionsexecutable by a processor for statistically equivalent level of safetymodeling. In the illustrated embodiment, the computer instructionsinclude a component/aircraft reliability module 28, an equivalent fleetreliability module 30 and a credit validation module 32. It is to beunderstood by those skilled in the art that these and other modulesexecuted by statistically equivalent level of safety modeling computingsystem 26 may be implemented in a variety of forms including hardware,software, firmware, special purpose processors and combinations thereof.

Referring to FIG. 2 in the drawings, therein is depicted a graphillustrating a probability distribution relating to the reliability of acomponent or aircraft in an aircraft fleet that is generally designated40. As illustrated, the probability distribution is a normaldistribution wherein the number of component failures is time dependentthus, the probability distribution is a time dependent probabilitydistribution and more specifically, a time to failure probabilitydistribution that may be generated based upon fatigue factors 16including component strength 18, loads 20 and usage 22. Even though theillustrated probability distribution is a normal distribution, it shouldbe understood by those skilled in the art that any probabilitydistribution of discrete and/or continuous random variables including,but not limited to, lognormal distributions and Poisson distributionsmay alternatively be used. In general, reliability may be defined as theprobability that an item or system will operate in a satisfactory mannerfor a specified period of time when used under a specific set ofconditions including environmental and operational conditions. In thepresent disclosure, it will sometimes be more illustrative to discussreliability in terms of unreliability, wherein unreliability is thecomplement of reliability and wherein unreliability may be referred toas the probability of failure. In both cases, reliability andunreliability are generally a function of time with reliabilitydecreasing over time and unreliability increasing over time. Asillustrated in FIG. 2, the time to failure for a component is quantifiedin a probability distribution 42, wherein the reliability (p) at a givenpoint in time (t) is the area 44 under probability distribution curve 42to the right of timeline 46 and the unreliability (Q) is the area 48under probability distribution curve 42 to the left of timeline 46. Ascan be seen, reliability decreases as timeline 46 move to the rightwhile unreliability increases as timeline 46 move to the right, whereinthe relationship between unreliability (Q) and reliability (p) isdetermined according to the formula:

(Q)=1−(p).

It should be noted that for component reliability, two approaches arecommonly used; namely, actuarial and physical. In actuarial reliabilityanalysis, component failures are tracked to build models to predictfuture failures. In the case of aircraft structural component failures,however, actuarial reliability analysis cannot be relied upon, as actualfailures of structural components would lead to an unacceptable level ofsafety. Accordingly, for such critical components, physical reliabilityanalysis, which relies upon physical models not failure data, is usedfor reliability prediction.

In reliability analysis of a system, such as an aircraft, the system ismade of multiple components, such as rotors, rotor drive systems betweenthe engines and rotor hubs, controls, fuselage, fixed and movablecontrol surfaces, engine and transmission mountings, landing gear, andtheir related primary attachments. The overall structure of a systemplays a key role in determining the impact of a component's reliabilityon the whole of the system. Two basic structures can be used torepresent most systems; namely, parallel structures and seriesstructures. In a parallel structure, a system is said to be functioningif at least one of its components is functioning thus forming aredundant system that continues to function as long as one of theparallel components continues to function. In other words, thereliability of a parallel system is at least as reliable as its mostreliable component. In a series structure, however, the system is saidto be functioning only if all of its components are functioning, forexample, the reliability of a chain is most influenced by its weakestlink. In other words, the reliability of a series structure is at mostas reliable as its least reliable component.

Applying the system reliability model to aircraft, each aircraft can beconsidered the system and each critical aircraft component can beconsidered a component in the system. Likewise, an aircraft fleet can beconsidered the system and each aircraft can be considered a component inthe system. For the purposes of structural reliability and thereforesafety of an aircraft fleet, the series structure is the best-suitedsystem reliability model as the fleet is only as reliable as its leastreliable aircraft. It is noted that this approach is consistent withsafe-life fatigue methodology 12 discussed above which assumes reducedstrength (mean −3 sigma), highest flight loads and usage “as severe asexpected in service.” In other words, safe-life fatigue methodology 12should generate a component life limit that guarantees the leastreliable aircraft is still highly reliable and safe. Accordingly,safe-life fatigue methodology 12 can be used to establish a baselinefleet reliability and modifications to this model can be used toevaluate changes in fleet reliability.

Using the series structure for system reliability of an aircraft fleetwill now be described with reference to FIG. 3. The system reliabilityof a series structure of independent components is the product of thereliability of the components. For example, if three components in aseries structure have reliability values of 0.99, 0.999, and 0.9999respectively, then the system has a reliability of0.99×0.999×0.9999=0.9889. It should be noted that the product of theindividual reliabilities is slightly less than the reliability of thecomponent with the lowest reliability in the system. If all of thecomponents can be modeled as having the same reliability, then thesystem reliability of the series structure of order n becomes:

(p _(S))=(p _(C))^(n)

where (p_(S)) is the system reliability, (p_(C)) is the individualcomponent reliability and (n) is the population size or number ofcomponents. In the aircraft fleet reliability example, the system is theaircraft fleet, the components are individual aircraft and thepopulation size is the number of aircraft in the fleet. In the case of afleet of 100 aircraft with an aircraft unreliability of (Q_(C))=1×10⁻⁶or reliability of (p_(C))=0.999999, the fleet reliability would be:

(p _(S))=(p _(C))¹⁰⁰=(0.999999)¹⁰⁰=0.9999,

which represents a fleet probability of failure or system unreliabilityof (Q_(S))=1×10⁻⁴. In the present analysis, those skilled in the artwill recognize that an aircraft is made of multiple critical components,which may each have more than one failure mode. Assuming each of thesecritical components is structurally independent from the others, thecomponents may be viewed a series structure, wherein any component couldaffect the entire aircraft. Accordingly, the present analysis willdiscuss aircraft reliability in terms of the portion of the aircraftreliability due to a specific component's reliability.

In the aircraft example presented, all aircraft have been assumed tohave the same reliability. Usage monitoring, however, has shown thatthere exists a wide variation between “normal” usage and “usage assevere as expected.” Based upon these differences, an aircraft fleet maybe split into multiple sub-fleets based upon usage profiles. Forexample, using Health and Usage Monitoring System (HUMS) data, one ormore usage profiles can be identified from the measured data. As bestseen in FIG. 3, an aircraft fleet 50 having a fleet population of (n)aircraft has been split two groups or sub-fleets denoted as sub-fleet(A) and sub-fleet (B). In sub-fleet (A) there are (m) aircraft, where(m)<(n), and in sub-fleet (B) there are (n-m) aircraft. When multiplesub-fleets are included with a fleet, the fleet reliability isdetermined by combining the sub-fleet reliabilities on a weighted basis.For example, if all of the aircraft in sub-fleet (A) have a reliabilityvalue of (p_(A)) and all of the aircraft in sub-fleet (B) have areliability value of (p_(B)), the fleet reliability (p_(F)) would bedetermined according to the formula:

(p _(F))=(p _(A))^(m)×(p _(B))^(n-m)

wherein, the contribution of each sub-fleet to the overall fleetreliability is quantified as a function of (1) the reliabilityassociated with the usage profile for each sub-fleet and (2) the size ofeach sub-fleet. Thus, to determine fleet reliability, the reliabilityvalue associated with each of the sub-fleets must be determined. Thesystems and methods of statistically equivalent level of safety modelingdisclosed herein use known and/or assumed distributions of strength 18,loads 20 and usage 22, as best seen in FIG. 1, to generate componenttime to failure probability distribution functions, such as that shownin FIG. 2, from which reliability values may be determined.

Referring additionally to FIG. 4A, two graphs are depicted illustratingprobability distributions relating to sub-fleet (A) and sub-fleet (B),respectively. For example, component/aircraft reliability module 28 maybe used to generate time to failure probability distribution functionsusing a Monte Carlo simulation, Monte Carlo with importance sampling,Markov Chain Monte Carlo simulation, First and Second Order ReliabilityMethods (FORM/SORM), convolution methods or other suitable probabilistictechnique to generate probability distributions representative of thecomponent time to failure functions. The upper graph in FIG. 4Arepresents a component time to failure probability distribution function60 for a severe usage profile associated with sub-fleet (A). In theillustrated embodiment, probability distribution function 60 is a normaldistribution having a mean of 10,000 hours and a standard deviation of1,000 hours. Based upon retirement time 24 of safe-life fatiguemethodology 12 or other suitable fatigue analysis, the location of alife limit timeline 62 has been determined to be 5,000 hours. Asillustrated, the area 64 under probability distribution curve 60 to theright of life limit timeline 62 represents the reliability of thecomponent at the life limit of 5,000 hours. The area 64 can bedetermined by identifying the location of life limit timeline 62relative to the mean of the normal distribution in terms of standarddeviations according to the formula:

Life Limit=Mean−(x)(standard deviation).

In this case, the life limit is 5,000 hours, the mean is 10,000 and thestandard deviation is 1,000 hours. Solving for (x) the formula becomes:

(x)=(Mean−Life Limit)/(standard deviation)=(10,000−5,000)/(1,000)=5

In this case, life limit timeline 62 is 5 standard deviations (5 sigma)from the mean which corresponds to a reliability value (p_(A)) forsub-fleet (A) of 0.999 993, which can be represented as (0.9₅3) meaningfive (9_(S)) following the decimal point.

The lower graph in FIG. 4A represents a component time to failureprobability distribution function 66 for a normal usage profileassociated with sub-fleet (B). In the illustrated embodiment,probability distribution function 66 is a normal distribution having amean of 15,000 hours and a standard deviation of 1,500 hours. Asillustrated, the area 68 under probability distribution curve 66 to theright of life limit timeline 62 represents the reliability of thecomponent at the life limit of 5,000 hours. The area 68 can bedetermined according to the formula:

(x)=(Mean−Life Limit)/(standard deviation)=(15,000−5,000)/(1,500)=6.667

In this case, life limit timeline 62 is 6.667 standard deviations (6.667sigma) from the mean which corresponds to a reliability value (p_(B))for sub-fleet (B) of 0.999 999 999 02 or (0.9₉02).

Using, for example, equivalent fleet reliability module 30, the baselinefleet reliability (p_(F)) can be determined for a fleet comprised ofsub-fleet (A) with reliability value (p_(A))=(0.9₅3) and a population of25 aircraft and sub-fleet (B) with reliability value (p_(B))=(0.9₉02)and a population of 75 aircraft according to the formula:

(p _(F))=(p _(A))^(m)×(p _(B))^(n-m)=(0.9₅3)²⁵×(0.9₉02)⁷⁵=0.999 992 83or (0.9₅283)

Importantly, this fleet reliability methodology can be used to comparemultiple scenarios such as the baseline fleet reliability and apost-credit fleet reliability such that a proposed usage credit can beevaluated in, for example, credit validation module 32. As illustratedin FIG. 4A, the baseline fleet reliability was generated using thesevere usage profile of sub-fleet (A) to establish the life limit forboth sub-fleet (A) and sub-fleet (B). As best seen in FIG. 4B, sub-fleet(A) retains the life limit of 5,000 hours represented by life limittimeline 62 and thus the reliability value of sub-fleet (A) remains(p_(A))=0.999 993 or (0.9₅3). Sub-fleet (B) has been given a credit of1,000 hours based upon having a normal usage profile and is nowdesignated sub-fleet (B/C) to indicate the credit. As illustrated, thecredit shifts the life limit to 6,000 hours, represented by the shiftbetween life limit timeline 62 and life limit timeline 70. Asillustrated, the area 72 under probability distribution curve 66 to theright of life limit timeline 70 represents the reliability of thecomponent at the life limit of 6,000 hours. The area 70 can bedetermined according to the formula:

(x)=(Mean−Life Limit)/(standard deviation)=(15,000−6,000)/(1,500)=6

In this case, life limit timeline 70 is 6 standard deviations (6 sigma)from the mean which corresponds to a post-credit reliability value(p_(BC)) for sub-fleet (B) of 0.999 999 926 or (0.9₇26).

Using, for example, equivalent fleet reliability module 30, thepost-credit fleet reliability (p_(FC)) can be determined for a fleetcomprised of sub-fleet (A) with reliability value (p_(A))=(0.9₅3) and apopulation of 25 aircraft and sub-fleet (B/C) with reliability value(p_(BC))=(0.9₇26) and a population of 75 aircraft according to theformula:

(p _(FC))=(p _(A))^(m)×(p _(BC))^(n-m)=(0.9₅3)²⁵×(0.9₇26)⁷⁵=0.999 992 76or (0.9₅276)

Using credit validation module 32, for example, it can be seen that thelife limit shift applied to sub-fleet (B) had a slight impact on theoverall fleet reliability; namely, baseline fleet reliability(p_(F))=(0.9₅283) and post-credit fleet reliability (p_(FC))=(0.9₅276)which is a difference of (7.399×10⁻⁸) or (0.000007%). In comparing thebaseline fleet reliability (p_(F)) to the post-credit fleet reliability(p_(FC)), it is clear that the change in fleet reliability is verysmall. Given the magnitude of the numbers, however, it is more revealingto compare baseline fleet unreliability (Q_(F)) with the post-creditfleet unreliability (Q_(FC)) wherein, baseline fleet unreliability is:

(Q _(F))=(1−(p _(F)))=(1−(0.9₅283))=(7.16626×10⁻⁶);

and post-credit fleet unreliability is:

(Q _(FC))=(1−(p _(FC)))=(1−(0.9₅276))=(7.24026×10⁻⁶);

which is a difference of 7.399×10⁻⁸ or (1.0%). In the present example,the resulting difference in fleet unreliability is measured against apredetermined threshold value that is selected to yield a statisticallyequivalent level of fleet safety. If the resulting difference in fleetunreliability is within the allowable threshold of change, then thecredit added to sub-fleet (B) for having a normal usage profile isvalidated and considered a safe usage credit. If on the other hand, theresulting difference in fleet unreliability is not within the allowablethreshold of change, then the credit added to sub-fleet (B) is notvalidated and should be adjusted. In the present example, if the (1.0%)difference in fleet unreliability is within the allowable threshold ofchange, then the credit of 1,000 hours given to sub-fleet (B) isvalidated but, if the (1.0%) difference in fleet unreliability isoutside the allowable threshold of change, then the credit of 1,000hours given to sub-fleet (B) is not validated.

Even though the present example has been based upon splitting anaircraft fleet into two aircraft sub-fleets, it should be understood bythose skilled in the art that the systems and methods of statisticallyequivalent level of safety modeling disclosed herein are not limited toaircraft fleets and are not limited to having only two sub-fleets. Infact, the systems and methods of statistically equivalent level ofsafety modeling disclosed herein are beneficial for use relating to anytype of system having structural components subject to fatigue failure,having maintenance schedules and/or having life limits. In addition, afleet or system may be split into more than two groups based upon avariety factors such as the usage profiles in the present example.Further, each such group may receive a varying grade of credit basedupon the differences in the factors defining the groups such asdifferences in the usage profiles.

Those skilled in the art will also understand that the use of this“relative reliability” approach produces a valid comparison as long asthe assumptions used while generating baseline and post-credit fleetreliability are applicable. For example, even though load variability issometimes difficult to quantify, if the same assumptions for loadvariability are used in both the baseline and post-credit fleetreliability cases, then the relative impact of the usage credit can beevaluated without concern for the absolute validity of the assumption solong as load variability is reasonably independent from usage. In thismanner, the load variability assumptions used in both the baseline andpost-credit fleet reliability cases “cancel out” in the end result.

Referring now to FIG. 5 of the drawings, a graph illustrates the fleetunreliability sensitivity to credit given to a sub-fleet. Continuingwith the example presented above, when sub-fleet (B) is given a creditof 1,000 hours based upon having a normal usage profile and sub-fleet(A) is given no credit based upon having a severe usage profile, theresulting post-credit fleet unreliability is (Q_(FC))=(7.24026×10⁻⁶)which is a (1.0%) difference from the baseline fleet unreliability(Q_(F))=(7.16626×10⁻⁶) as indicated by data point 80. Using the systemsand methods for statistically equivalent level of safety modelingdisclosed herein, additional data points, trend data and sensitivityinformation can be generated. For example, fleet unreliabilitysensitivity can be determined by processing a plurality of credit levelsas described above. As illustrated, if sub-fleet (B) is given a creditof 500 hours instead of 1,000 hours, the resultant difference betweenpost-credit fleet unreliability and baseline fleet unreliability isapproximately (0.1%) as indicated by data point 82. Similarly, ifsub-fleet (B) is given a credit of 1500 hours instead of 1,000 hours,the resultant difference between post-credit fleet unreliability andbaseline fleet unreliability is approximately (8.5%) as indicated bydata point 84 and if sub-fleet (B) is given a credit of 2000 hoursinstead of 1,000 hours, the resultant difference between post-creditfleet unreliability and baseline fleet unreliability is approximately(50%) as indicated by data point 86. Together, data points 80, 82, 84and 86 define a trend line 88 that can be used as an aid in selecting asafe usage credit that is within the predetermined threshold, thusyielding a statistically equivalent level of safety in post-credit fleetunreliability when compared to baseline fleet unreliability. Such atrend line is also useful in determining how sensitive the fleetunreliability is to changes in the credit value. For example, in ahighly sensitive system, it may be desirable to select a moreconservative credit or to reset the predetermined threshold.

Similar methods may be used to test fleet unreliability sensitivity toother variables. For example, as best seen in FIG. 6 of the drawings, agraph illustrates the fleet unreliability sensitivity to changes in thepopulation ratio of the sub-fleets. Continuing with the examplepresented above, trend line 88 has been reproduced illustrating thechange in fleet unreliability based upon changes in the credit given tosub-fleet (B) for a fleet having a population of 25 aircraft insub-fleet (A) and 75 aircraft in sub-fleet (B). Using the systems andmethods for statistically equivalent level of safety modeling disclosedherein, additional data points, trend data and sensitivity informationcan be generated. For example, trend line 90 represents credit given tosub-fleet (B) in a fleet having a population of 10 aircraft in sub-feet(A) and 90 aircraft in sub-fleet (B). Similarly, trend line 92represents credit given to sub-fleet (B) in a fleet having a populationof 2 aircraft in sub-feet (A) and 98 aircraft in sub-fleet (B). Asillustrated, as the population in the sub-fleet receiving credit goesup, the difference between the baseline fleet unreliability and thepost-credit fleet unreliability also goes up. For example, as indicatedat data point 80, when sub-fleet (B) is given a credit of 1,000 hoursand sub-fleet (A) is given no credit, the resulting difference betweenpost-credit fleet unreliability and baseline fleet unreliability is(1.0%). As indicated by data point 94, for a 1,000 hour credit given tosub-fleet (B), when sub-fleet (A) has 10 aircraft and sub-feet (B) has90 aircraft, the resultant difference between post-credit fleetunreliability and baseline fleet unreliability is approximately (3%).Likewise, as indicated by data point 96, for a 1,000 hour credit givento sub-fleet (B), when sub-fleet (A) has 2 aircraft and sub-fleet (B)has 98 aircraft, the resultant difference between post-credit fleetunreliability and baseline fleet unreliability is approximately (20%).Similarly, as indicated by data point 98, if the threshold of change toyield a statistically equivalent level of safety in post-credit fleetunreliability when compared to baseline fleet unreliability ispredetermined to be (1%), for a fleet having 10 aircraft in sub-fleet(A) and 90 aircraft in sub-fleet (B), the maximum safe usage credit isabout 750 hours.

Referring now to FIG. 7 of the drawings, one embodiment of a process forstatistically equivalent level of safety modeling relating to aircraftcomponents of aircraft within an aircraft fleet will now be described.The first step of the process involves defining usage profiles asindicated in block 100. Usage profiles may be component dependent, so afirst part of this portion of the process may involve identifyingcandidate components. Once selected, a review of the baseline fatiguesubstantiation for the component including, for example, review ofsafe-life fatigue methodology 12, will determine what parameters mostinfluence the fatigue life. Once determined, a usage threshold orthresholds must be established which categorize all aircraft in thefleet into one and only one usage profile, as indicated in block 102.

For example, density altitude may be a parameter that correlates tofatigue damage to a selected component resulting in a baseline fatigueretirement life of 10,000 hours. If it is shown from the baselinefatigue substantiation that there is a significant difference in fatiguedamage above a certain density altitude threshold, such as significantfatigue damage above 6,000 feet density altitude, but no fatigue damagebelow 6,000 feet density altitude, then this forms a suitable thresholdbetween usage states. Any aircraft, however, could spend some time aboveand some time below the 6,000 feet threshold on a given flight. Toensure aircraft can only be categorized into a single group, the timedimension must be considered. As best seen in FIG. 8, flight time foraircraft at high altitude is represented by the vertical axis and totalflight time is represented by the horizontal axis, wherein the highaltitude state corresponds to the 6,000 feet threshold. An aircraft thatspends all of its time in high altitude would be represented by usageprofile line 104 and an aircraft that spends 50% of its time at highaltitude would be represented by usage profile line 106. Thus, at 10,000hours of total flight time, a component subject to density altituderelated fatigue damage at high altitude in an aircraft having usageprofile 104 would have reached the 10,000 hours life limit of thatcomponent for high altitude flight. The same component in an aircrafthaving usage profile 106, however, would have only experienced 5,000hours of high altitude fight time in its 10,000 hours of total flighttime. Utilizing this information, sub-fleets can be defined that includeall aircraft in the fleet. For example, a sub-fleet (A) could be definedby the usage profile of spending between 50% and 100% of fight time athigh altitude. Similarly, a sub-fleet (B) could be defined by the usageprofile of spending between 0% and 50% of flight time at high altitude.

Returning to FIG. 7, the next step in the process involves thecalculation of the structural reliability for each identified sub-fleetas indicated in block 108. This step generates time to failureprobability distribution functions for each sub-fleet, as describedabove with reference to FIG. 4A. Component fatigue substantiation;namely, strength 18, loads 20 and usage 22, provide inputs to thisprocess, as best seen in FIG. 9. The component strength variability andloads variability information typically come from the safe-life fatiguemethodology 12 and usage variability may be estimated. For example,estimating usage distribution involves a characterization of actualfleet operations or, in the case of a new aircraft design, expectedfleet operations based upon data from other operational aircraft. For anexisting aircraft, HUMS data recorded from the fleet may be used forthis purpose. It should be noted that any estimate should take intoconsideration the frequency of occurrence spectrum based uponinformation that is applicable to the missions flown by the fleet. Next,component/aircraft reliability module 28 may be used to generate time tofailure probability distribution functions for each sub-fleet, referredto as component reliability in block 110.

Referring again to FIG. 7, the next step in the process involves thecalculation of the baseline fleet reliability as indicated in block 112.This process may occur within equivalent fleet reliability module 30.The component reliability information 110 is now combined with fleetusage distribution information 114 (see discussion referencing FIG. 8)to establish a fleet reliability model 116, as best seen in FIG. 10. Thefleet reliability model 116 includes the population of each sub-fleet byactual count or by percentage as well as the time to failure probabilitydistribution functions for each sub-fleet. This information is used todetermine the reliability value for each sub-fleet in block 118. Thisinvolves using the baseline fatigue retirement life 24 from thesafe-life fatigue methodology 12 in combined with the time to failureprobability distribution functions of each sub-fleet as described abovewith reference to FIG. 4A. For example, in a fleet of (n) aircraft, (m)aircraft are selected for inclusion in sub-fleet (A) based upon spending50%-100% of their flight time at high altitude while (n-m) aircraft areselected for inclusion in sub-fleet (B) based upon spending 0%-50% oftheir flight time at high altitude. If a component subject to densityaltitude related fatigue damage at high altitude has a life limit of10,000 hours, both sub-fleet (A) and sub-fleet (B) are assigned thislife limit. The component and/or aircraft reliability value for eachsub-fleet is now determined by processing the life limit informationtogether with the time to failure probability distribution functions ofeach sub-fleet, as described above with reference to FIG. 4A. Thebaseline fleet reliability is now determined in block 120 by combiningthe sub-fleet reliability values on a weighted basis such as bymultiplying together the sub-fleet reliability values raised to thesub-fleet population for each aircraft sub-fleet, as described abovewith reference to FIG. 4A.

The next step in the process of FIG. 7 is applying a usage credit toselected sub-fleets as indicated in block 122. This process involvesdetermining which sub-fleet or sub-fleets should receive credit and thetype of credit to be applied. For example, in the previous discussion,the credit has involved a shift in the life limit, which grants asingular amount of credit to all members of a population group, the1,000 hour credit applied to sub-fleet (B) as described above withreference to FIG. 4B. In addition to shifting the entire group by a setamount of credit, another credit options include applying a factor tothe usage of one or more sub-fleets. For example, a credit factor wouldbe to count every hour as less than one hour of “equivalent time.” If afactor of 0.8 were determined to be appropriate, then 5,000 hours ofactual usage would equate to 5,000 hours×0.8=4,000 hours of equivalentusage, which is an effective credit of 1,000 hours. Once a value for thecredit is proposed, a complete usage proposal can be stated such as “Acredit shift of 1,000 hours is proposed for all aircraft in sub-fleet(B).”

Post-credit fleet reliability can now be determined as indicated inblock 124. This process may occur within equivalent fleet reliabilitymodule 30. The component reliability information 110, fleet usagedistribution information 114 and fleet reliability model 116, previousgenerated are used again as best seen in FIG. 11. The fleet reliabilitymodel 116 includes the population of each sub-fleet by actual count orby percentage as well as the time to failure probability distributionfunctions for each sub-fleet. This information is used to determine thepost-credit reliability value for each sub-fleet in block 128. Thisinvolves using the baseline fatigue retirement life 24 from thesafe-life fatigue methodology 12 in combined with the time to failureprobability distribution functions of each sub-fleet that does notreceive a credit as described above with reference to FIG. 4B. Inaddition, a credit-based life limit from block 126 is used in combinedwith the time to failure probability distribution functions of eachsub-fleet receiving a credit as described above with reference to FIG.4B. For example, in a fleet of (n) aircraft, (m) aircraft are selectedfor inclusion in sub-fleet (A) based upon spending 50%-100% of theirflight time at high altitude while (n-m) aircraft are selected forinclusion in sub-fleet (B) based upon spending 0%-50% of their flighttime at high altitude. If a component subject to density altituderelated fatigue damage at high altitude has a life limit of 10,000hours, sub-fleet (A) is assigned this life limit but sub-fleet (B) isgiven a credit of 1,000 hours. The component and/or aircraft post-creditreliability value for each sub-fleet is now determined by processing thelife limit information together with the time to failure probabilitydistribution functions of each sub-fleet, as described above withreference to FIG. 4B. The post-credit fleet reliability is nowdetermined in block 130 by combining the sub-fleet reliability values ona weighted basis such as by multiplying together the sub-fleetreliability values raised to the sub-fleet population for each aircraftsub-fleet, as described above with reference to FIG. 4B.

Returning to FIG. 7, the next step in the process involves comparing thebaseline fleet reliability with the post-credit fleet reliability asindicated in block 132. This process may occur within credit validationmodule 32. Taking the example from FIGS. 4A-4B, adding the life limitshift to sub-fleet (B) had a slight impact on the overall fleetreliability which can be quantified as the difference between baselinefleet reliability (p_(F))=(0.9₅283) and post-credit fleet reliability(p_(FC))=(0.9₅276) which is (7.399×10⁻⁸) or (0.000007%). Making the samecomparison using fleet unreliability yields the difference betweenbaseline fleet unreliability (Q_(F))=(7.16626×10⁻⁶) and post-creditfleet unreliability (Q_(FC))=(7.24026×10⁻⁶) is (7.399×10⁻⁸) or (1.0%).Once the change in overall fleet unreliability has been determined, itis compared to the predetermined threshold in decision block 134.Preferably, the predetermined threshold is selected such thatpost-credit fleet reliability and baseline fleet reliability have astatistically equivalent level of safety. In the present example, if the(1.0%) difference in fleet unreliability is within the predeterminedthreshold, then the credit of 1,000 hours given to sub-fleet (B) isvalidated and the process is complete. If, however, the (1.0%)difference in fleet unreliability is outside the predeterminedthreshold, then the credit of 1,000 hours given to sub-fleet (B) is notvalidated and a modified credit may be proposed as indicated in block136. The process would return to block 122 enabling the modified creditto be tested in and potentially validated by the statisticallyequivalent level of safety modeling process of the present disclosure.

Embodiments of methods, systems and program products of the presentdisclosure have been described herein with reference to drawings. Whilethe drawings illustrate certain details of specific embodiments thatimplement the methods, systems and program products of the presentdisclosure, the drawings should not be construed as imposing on thedisclosure any limitations that may be present in the drawings. Theembodiments described above contemplate methods, systems and programproducts stored on any non-transitory machine-readable storage media foraccomplishing its operations. The embodiments may be implemented usingan existing computer processor or by a special purpose computerprocessor incorporated for this or another purpose or by a hardwiredsystem.

Certain embodiments can include program products comprisingnon-transitory machine-readable storage media for carrying or havingmachine-executable instructions or data structures stored thereon. Suchmachine-readable media may be any available media that may be accessedby a general purpose or special purpose computer or other machine with aprocessor.

By way of example, such machine-readable storage media may comprise RAM,ROM, EPROM, EEPROM, CD-ROM or other optical disk storage, magnetic diskstorage or other magnetic storage devices, or any other medium which maybe used to carry or store desired program code in the form ofmachine-executable instructions or data structures and which may beaccessed by a general purpose or special purpose computer or othermachine with a processor. Combinations of the above are also includedwithin the scope of machine-readable media. Machine-executableinstructions comprise, for example, instructions and data which cause ageneral purpose computer, special purpose computer or special purposeprocessing machines to perform a certain function or group of functions.

Embodiments of the present disclosure have been described in the generalcontext of method steps which may be implemented in one embodiment by aprogram product including machine-executable instructions, such asprogram code, for example in the form of program modules executed bymachines in networked environments. Generally, program modules includeroutines, programs, logics, objects, components, data structures, andthe like that perform particular tasks or implement particular abstractdata types. Machine-executable instructions, associated data structuresand program modules represent examples of program code for executingsteps of the methods disclosed herein. The particular sequence of suchexecutable instructions or associated data structures representsexamples of corresponding acts for implementing the functions describedin such steps.

Embodiments of the present disclosure may be practiced in a networkedenvironment using logical connections to one or more remote computershaving processors. Those skilled in the art will appreciate that suchnetwork computing environments may encompass many types of computers,including personal computers, hand-held devices, multi-processorsystems, microprocessor-based or programmable consumer electronics,network PCs, minicomputers, mainframe computers, and so on. Embodimentsof the disclosure may also be practiced in distributed computingenvironments where tasks are performed by local and remote processingdevices that are linked through a communications network includinghardwired links, wireless links and/or combinations thereof. In adistributed computing environment, program modules may be located inboth local and remote memory storage devices.

An exemplary implementation of embodiments of methods, systems andprogram products disclosed herein might include general purposecomputing computers in the form of computers, including a processingunit, a system memory or database, and a system bus that couples varioussystem components including the system memory to the processing unit.The database or system memory may include read only memory (ROM) andrandom access memory (RAM). The database may also include a magnetichard disk drive for reading from and writing to a magnetic hard disk, amagnetic disk drive for reading from or writing to a removable magneticdisk and an optical disk drive for reading from or writing to aremovable optical disk such as a CD ROM or other optical media. Thedrives and their associated machine-readable media provide nonvolatilestorage of machine-executable instructions, data structures, programmodules and other data for the computer. User interfaces, as describedherein may include a computer with monitor, keyboard, a keypad, a mouse,joystick or other input devices performing a similar function.

It should be noted that although the diagrams herein may show a specificorder and composition of method steps, it is understood that the orderof these steps may differ from what is depicted. For example, two ormore steps may be performed concurrently or with partial concurrence.Also, some method steps that are performed as discrete steps may becombined, steps being performed as a combined step may be separated intodiscrete steps, the sequence of certain processes may be reversed orotherwise varied, and the nature or number of discrete processes may bealtered or varied. The order or sequence of any element or apparatus maybe varied or substituted according to alternative embodiments.Accordingly, all such modifications are intended to be included withinthe scope of the present disclosure. Such variations will depend on thesoftware and hardware systems chosen and on designer choice. It isunderstood that all such variations are within the scope of the presentdisclosure. Likewise, software and web implementations of the presentdisclosure could be accomplished with standard programming techniquesusing rule based logic and other logic to accomplish the variousprocesses.

The foregoing description of embodiments of the disclosure has beenpresented for purposes of illustration and description. It is notintended to be exhaustive or to limit the disclosure to the precise formdisclosed, and modifications and variations are possible in light of theabove teachings or may be acquired from practice of the disclosure. Theembodiments were chosen and described in order to explain the principalsof the disclosure and its practical application to enable one skilled inthe art to utilize the disclosure in various embodiments and withvarious modifications as are suited to the particular use contemplated.Other substitutions, modifications, changes and omissions may be made inthe design, operating conditions and arrangement of the embodimentswithout departing from the scope of the present disclosure. Suchmodifications and combinations of the illustrative embodiments as wellas other embodiments will be apparent to persons skilled in the art uponreference to the description. It is, therefore, intended that theappended claims encompass any such modifications or embodiments.

What is claimed is:
 1. A statistically equivalent level of safetymodeling method for structural components of aircraft within an aircraftfleet having (n) aircraft, the method comprising: (A). identifying afirst aircraft sub-fleet based upon a first usage profile and a secondaircraft sub-fleet based upon a second usage profile, the first aircraftsub-fleet having (m) aircraft and the second aircraft sub-fleet having(n-m) aircraft; (B). determining a first reliability value (p₁) for thefirst aircraft sub-fleet and a second reliability value (p₂) for thesecond aircraft sub-fleet; (C). determining a baseline fleet reliability(p_(f1)) for the aircraft fleet according to the formula:(p_(f1))=(p₁)^(m)×(p₂)^(n-m); (D). applying a credit to the secondaircraft sub-fleet; (E). determining a post-credit reliability value(p_(2C)) for the second aircraft sub-fleet based upon the credit; (F).determining a post-credit fleet reliability (p_(f2)) for the aircraftfleet according to the formula: (p_(f2))=(p₁)^(m)×(p_(2C))^(n-m); (G).comparing the baseline fleet reliability (p_(f1)) with the post-creditfleet reliability (p_(f2)) to identify a change in fleet reliability;and (H). determining whether the change in fleet reliability is within apredetermined threshold to validate the credit applied to the secondaircraft sub-fleet.
 2. The method as recited in claim 1 wherein theusage profiles further comprise measured usage levels.
 3. The method asrecited in claim 1 wherein the second usage profile further comprises aless extreme usage profile than the first usage profile.
 4. The methodas recited in claim 1 wherein the reliability values further comprisetime dependent probability distribution functions.
 5. The method asrecited in claim 1 wherein the reliability values further comprise timeto failure probability distribution functions.
 6. The method as recitedin claim 1 wherein the reliability values further comprise probabilitydistribution functions selected from the group consisting of probabilitydistribution functions of discrete random variables, probabilitydistribution functions of continuous random variables, normaldistribution functions, lognormal distribution functions and Poissondistribution functions.
 7. The method as recited in claim 1 wherein thereliability values relate to one or more structural components of theaircraft of the first and second aircraft sub-fleets.
 8. The method asrecited in claim 1 wherein the reliability values further compriseprobability distribution functions based upon strength, loads and usageof the aircraft of the first and second aircraft sub-fleets.
 9. Themethod as recited in claim 1 wherein the credit is selected from thegroup consisting of life limit shifts, life factors and combinationthereof.
 10. The method as recited in claim 1 further comprisingapplying a revised credit if the change in fleet reliability is notwithin the predetermined threshold and repeating steps (E)-(H).
 11. Astatistically equivalent level of safety modeling method for structuralcomponents of aircraft within an aircraft fleet, the method comprising:(A). identifying aircraft sub-fleets within the aircraft fleet basedupon aircraft usage profiles, each aircraft sub-fleet having a sub-fleetpopulation; (B). determining a sub-fleet reliability value for eachaircraft sub-fleet; (C). determining a baseline fleet reliability forthe aircraft fleet by multiplying together the sub-fleet reliabilityvalues raised to the sub-fleet population for each aircraft sub-fleet;(D). applying at least one credit to at least one aircraft sub-fleet;(E). determining a post-credit sub-fleet reliability value for eachaircraft sub-fleet based upon the at least one credit; (F). determininga post-credit fleet reliability for the aircraft fleet by multiplyingtogether the post-credit sub-fleet reliability values raised to thesub-fleet population for each aircraft sub-fleet; (G). comparing thebaseline fleet reliability with the post-credit fleet reliability toidentify a change in fleet reliability; and (H). determining whether thechange in fleet reliability is within a predetermined threshold tovalidate the at least one credit.
 12. The method as recited in claim 11wherein the usage profiles are based upon measured usage levels.
 13. Themethod as recited in claim 11 wherein the reliability values furthercomprise time dependent probability distribution functions.
 14. Themethod as recited in claim 11 wherein the reliability values furthercomprise probability distribution functions selected from the groupconsisting of probability distribution functions of discrete randomvariables, probability distribution functions of continuous randomvariables, normal distribution functions, lognormal distributionfunctions and Poisson distribution functions.
 15. The method as recitedin claim 11 wherein the reliability values relate to one or morestructural components of the aircraft of the aircraft sub-fleets. 16.The method as recited in claim 11 wherein the reliability values furthercomprise probability distribution functions based upon strength, loadsand usage of the aircraft of the aircraft sub-fleets.
 17. The method asrecited in claim 11 wherein the at least one credit is selected from thegroup consisting of life limit shifts, life factors and combinationthereof.
 18. The method as recited in claim 11 further comprisingapplying at least one revised credit to at least one aircraft fleet ifthe change in fleet reliability is not within the predeterminedthreshold and repeating steps (E)-(H).
 19. A statistically equivalentlevel of safety modeling method for structural components of a systemwithin a system fleet, the method comprising: (A). identifyingsub-fleets within the fleet based upon usage profiles; (B). determininga sub-fleet reliability value for each sub-fleet; (C). determining abaseline fleet reliability for the fleet by combining the sub-fleetreliability values on a weighted basis; (D). applying at least onecredit to at least one sub-fleet; (E). determining a post-creditsub-fleet reliability value for each sub-fleet based upon the at leastone credit; (F). determining a post-credit fleet reliability for thefleet by combining the post-credit sub-fleet reliability values on aweighted basis; (G). comparing the baseline fleet reliability with thepost-credit fleet reliability to identify a change in fleet reliability;and (H). determining whether the change in fleet reliability is within apredetermined threshold to validate the at least one credit.
 20. Themethod as recited in claim 19 further comprising establishing theweighted basis based upon the number of systems in each sub-fleet.